Download - MUNCHING SQUARES
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MUNCHING SQUARES
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A plot of the cells on a grid satisfying bitwise XOR (x, y) < n for consecutive values of n. n = 1, 2, .... grid size
It is thought that it was discovered by Jackson Wright on the RLE PDP-1 around 1962
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The colour of each pixel is determined by comparing the bit XOR (exclusive or) of its row and column indices with the selected threshold (n)
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The colour of each pixel is determined by comparing the bit XOR (exclusive or) of its row and column indices with the selected threshold (n)
Convert cell indices to binarySet n = 1
000 XOR000000Is 0 < 1?
![Page 5: MUNCHING SQUARES](https://reader035.vdocuments.mx/reader035/viewer/2022062304/568146f2550346895db42840/html5/thumbnails/5.jpg)
111
110
101
100
011
010
001
000
000 001 010 011 100 101 110 111
The colour of each pixel is determined by comparing the bit XOR (exclusive or) of its row and column indices with the selected threshold (n)
Convert cell indices to binarySet n = 1
000 XOR001001Is 1 < 1?
![Page 6: MUNCHING SQUARES](https://reader035.vdocuments.mx/reader035/viewer/2022062304/568146f2550346895db42840/html5/thumbnails/6.jpg)
111
110
101
100
011
010
001
000
000 001 010 011 100 101 110 111
The colour of each pixel is determined by comparing the bit XOR (exclusive or) of its row and column indices with the selected threshold (n)
Convert cell indices to binarySet n = 1
000 XOR010010Is 2 < 1?
![Page 7: MUNCHING SQUARES](https://reader035.vdocuments.mx/reader035/viewer/2022062304/568146f2550346895db42840/html5/thumbnails/7.jpg)
111
110
101
100
011
010
001
000
000 001 010 011 100 101 110 111
The colour of each pixel is determined by comparing the bit XOR (exclusive or) of its row and column indices with the selected threshold (n)
Convert cell indices to binarySet n = 1
![Page 8: MUNCHING SQUARES](https://reader035.vdocuments.mx/reader035/viewer/2022062304/568146f2550346895db42840/html5/thumbnails/8.jpg)
111
110
101
100
011
010
001
000
000 001 010 011 100 101 110 111
The colour of each pixel is determined by comparing the bit XOR (exclusive or) of its row and column indices with the selected threshold (n)
Convert cell indices to binarySet n = 1
001 XOR000001Is 1 < 1?
![Page 9: MUNCHING SQUARES](https://reader035.vdocuments.mx/reader035/viewer/2022062304/568146f2550346895db42840/html5/thumbnails/9.jpg)
111
110
101
100
011
010
001
000
000 001 010 011 100 101 110 111
The colour of each pixel is determined by comparing the bit XOR (exclusive or) of its row and column indices with the selected threshold (n)
Convert cell indices to binarySet n = 1
001 XOR001000Is 0 < 1?
![Page 10: MUNCHING SQUARES](https://reader035.vdocuments.mx/reader035/viewer/2022062304/568146f2550346895db42840/html5/thumbnails/10.jpg)
111
110
101
100
011
010
001
000
000 001 010 011 100 101 110 111
The colour of each pixel is determined by comparing the bit XOR (exclusive or) of its row and column indices with the selected threshold (n)
Convert cell indices to binarySet n = 1
![Page 11: MUNCHING SQUARES](https://reader035.vdocuments.mx/reader035/viewer/2022062304/568146f2550346895db42840/html5/thumbnails/11.jpg)
111
110
101
100
011
010
001
000
000 001 010 011 100 101 110 111
The colour of each pixel is determined by comparing the bit XOR (exclusive or) of its row and column indices with the selected threshold (n)
Convert cell indices to binary
Set n = 2
![Page 12: MUNCHING SQUARES](https://reader035.vdocuments.mx/reader035/viewer/2022062304/568146f2550346895db42840/html5/thumbnails/12.jpg)
111
110
101
100
011
010
001
000
000 001 010 011 100 101 110 111
The colour of each pixel is determined by comparing the bit XOR (exclusive or) of its row and column indices with the selected threshold (n)
Convert cell indices to binary
Set n = 3
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Good expressions:j ^ i < t (original munch squares)i == j^t((i | t) mod (j | t))j mod (t+1) == it&i^j < t|ii^j^t < i|j|tt div ~i == t div ~ji^j|t < j&ti^t^j mod 5j ^ i < i & tj & i < t ^ (t mod 3)(t div ~i^j) < (t div ~j^i)(i&t) mod ((j&t)+1)(i&t) mod ((j&t)+1) == ii^t+2&j
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My Favourite Booknot just coding
but
computational
thought